CONSISTENCY IN COVERAGE FOR 8 RANDOM SELECTIONS IN PICK 6, POOL 49 LOTTO
Colin Fairbrother
the highest coverage. You can test coverage if you don't have your own
utility by using Covermaster which you can get from the link in this
article: -
Manually Constructing a Best Lotto Wheel
http://lottoposter.com/forum_posts.asp?TID=609
Covermaster is not an RNG or Random Number Generator however you can
randomize a set of numbers that are isomorphic without changing the
Coverage. So, the following set -
01 02 03 04 05 06
07 08 09 10 11 12
13 14 15 16 17 18
19 20 21 22 23 24
25 26 27 28 29 30
31 32 33 34 35 36
37 38 39 40 41 42
43 44 45 46 47 48
which gives a 3if6 coverage of 14.82994 can be randomized as below and
still give the same coverage.
17 20 37 40 42 45
02 04 07 18 31 32
13 16 21 27 38 44
12 19 22 23 25 41
01 24 29 30 43 49
08 09 10 26 28 46
03 06 11 15 34 35
05 14 36 39 47 48
There is no better source of random numbers than the particular Lotto
game itself. Below are the coverage results for the UK Lotto game for
10 sets of 8 distinct draws starting from the first draw: -
Draws Coverage
1 to 8 13.96451
9 to 16 14.04514
17 to 24 14.20070
25 to 32 14.11467
33 to 40 13.82023
41 to 48 14.15297
49 to 56 13.68282
57 to 64 14.36345
65 to 72 13.72516
73 to 80 14.09675
Colin Fairbrother
http://LottoPoster.com
sm...@gmx.de
wrote:
> For 8 lines in a 6/49 Lotto game keeping the integers unique will give
> the highest coverage. You can test coverage if you don't have your own
> utility by using Covermaster which you can get from the link in this
> article: -
Collin, you are a liar.
> There is no better source of random numbers than the particular Lotto
> game itself.
What a big lie!
An optimised wheel randomized with Covermaster
like shown by yourself, gives a better random source
because it has a higher covering (like shown by yourself).
It has a lower number combination redundancy than any
other random number selection.method.
This is why you got the lotto idiocy award.
Thank you for proving that by yourself.
Colin Fairbrother
optimum coverage of 14.82994 is not impossible but highly unlikely.
After 7 lines with distinct integers there is only 7 lines from the
remaining 7 integers that would complete the set and this from
13,983,816 possibilities.
Continuing with the UK 6/49 Lotto game for another 10 sets with 8
draws sets we see the coverage is consistent.
Draw Range Coverage 3if6
81 to 88 13.80
89 to 96 13.94
97 to 104 13.98
105 to 112 14.12
113 to 120 14.06
121 to 128 14.07
129 to 136 13.95
137 to 144 13.81
145 to 152 13.82
153 to 160 13.95
The standard deviation is only 2.247 for the 20 sets.
Colin Fairbrother
http://LottoPoster.com
nigel
> On 16 Apr., 21:39, Colin Fairbrother <colin.fairbrot...@gmail.com>
> wrote:
>
>>For 8 lines in a 6/49 Lotto game keeping the integers unique will give
>>the highest coverage. You can test coverage if you don't have your own
>>utility by using Covermaster which you can get from the link in this
>>article: -
>>Manually Constructing a Best Lotto Wheelhttp://lottoposter.com/forum_posts.asp?TID=609
>>
>>Covermaster is not an RNG or Random Number Generator however you can
>>randomize a set of numbers that are isomorphic without changing the
>>Coverage. So, the following set -
>>01 02 03 04 05 06
>>07 08 09 10 11 12
>>13 14 15 16 17 18
>>19 20 21 22 23 24
>>25 26 27 28 29 30
>>31 32 33 34 35 36
>>37 38 39 40 41 42
>>43 44 45 46 47 48
>>which gives a 3if6 coverage of 14.82994 can be randomized as below and
>>still give the same coverage.
>>17 20 37 40 42 45
>>02 04 07 18 31 32
>>13 16 21 27 38 44
>>12 19 22 23 25 41
>>01 24 29 30 43 49
>>08 09 10 26 28 46
>>03 06 11 15 34 35
>>05 14 36 39 47 48
Purely as an intellectual exercise, since no intelligent gambler would
bet on all the numbers, it's interesting to consider those combos with a
view to guesstimating which would give the best chance of not sharing a
jackpot. There are 31 birthday numbers and 18 non-birthday numbers so it
is possible to generate 8 combinations which have the ideal mix for the
UK lottery, 4/2 or 3/3. Additionally, to circumvent the effects of
Benford's law, the birthday numbers in any particular combination should
have a relatively high average, close to the maximum of 16.5. I've
annotated the Covermaster randomised combos above - note that combos
with a birthday number average of above 16.5 have been rated as good
even though as a consequence other combos have birthday number averages
which are too low.
If anyone fancies writing software to filter out combos which are likely
to result in a shared jackpot, note that the above are only first-order
effects, and the filters may need to change from lottery to lottery to
reflect the sophistication of the players.
>>
>>There is no better source of random numbers than the particular Lotto
>>game itself. Below are the coverage results for the UK Lotto game for
>>10 sets of 8 distinct draws starting from the first draw: -
>>Draws Coverage
>> 1 to 8 13.96451
>> 9 to 16 14.04514
>>17 to 24 14.20070
>>25 to 32 14.11467
>>33 to 40 13.82023
>>41 to 48 14.15297
>>49 to 56 13.68282
>>57 to 64 14.36345
>>65 to 72 13.72516
>>73 to 80 14.09675
>>
>>Colin Fairbrotherhttp://LottoPoster.com
>
>
> Collin, you are a liar.
>
>
>>There is no better source of random numbers than the particular Lotto
>>game itself.
>
>
> What a big lie!
Since Colin hasn't revealed what he means by random, I can't support
that accusation. Also the original statement may be a non-sequitur,
completely out of context.
>
> An optimised wheel randomized with Covermaster
> like shown by yourself, gives a better random source
> because it has a higher covering (like shown by yourself).
>
> It has a lower number combination redundancy than any
> other random number selection.method.
I agree with those statements.
>
> This is why you got the lotto idiocy award.
> Thank you for proving that by yourself.
Can I nominate myself for a lotto idiocy award?
I've belatedly realised the trial I'm running won't actually support my
theory on the nature of randomness because the result of a positive
outcome will be equivocal.
Evil Nigel
Gerry
> Can I nominate myself for a lotto idiocy award?
You can do that but be advised Colin always wins.
Dionysus
wrote:
> For 8 lines in a 6/49 Lotto game keeping the integers unique will give
> the highest coverage. You can test coverage if you don't have your own
> utility by using Covermaster which you can get from the link in this
> article: -
why not find something consistancy for one filter.CM could be
understood as a filter for all combo.However,you can construct your
own combos in limited areas.
Jack Ricci
"nigel" wrote in message
news:4uWdndJ6SI_rkzbQ...@brightview.co.uk...
If anyone fancies writing software to filter out combos which are likely
to result in a shared jackpot, note that the above are only first-order
effects, and the filters may need to change from lottery to lottery to
reflect the sophistication of the players.
Evil Nigel
--------------------------------------------------------------------------------------------------------------------------
...It blows my mind to see that anyone would want to filter out the winning
of a shared jackpot.
Jack
nigel
It blows my mind that anyone would know the winning numbers in advance
so they'd know not to filter them out.
Evil Nigel
Gerry
Many years ago I applied some brute force filtering and would have won
jackpot if I had bought the 92 tickets but I didn't really believe in
the filtering method.
There was a lesson to be learned but I never figured it out because
I was and still am blown away.
All I have left of my shattered dream is a bunch of buttons to click :(
Jack Ricci
"nigel" wrote in message
news:EamdnXKrPLXkkzHQ...@brightview.co.uk...
Evil Nigel
------------------------------------------------------------------------------------------------------------------------------
That's a double negative...You are still hoping to filter out the combos
that would produce a shared jackpot. I would only do that if shared jackpots
occurred only once a decade, so as to need fewer combos to play each game
only if the past history data demonstrated that there would be a likelihood
of a shared jackpot combo not occurring in a draw but once in a decade, if
that were possible.
However, those shared jackpot combos do occur more often than just once
in a decade, and those shared-jackpot combos which your software ( or other
method of ) picks have just as good a likelihood of being drawn as the
actual combos which you eventually pay to play, so that makes your above
statements a redundant claim.
If you believe in or have faith in your number picking
scheme(s)/method(s), then the shared jackpot filter sucks.
Our Canadian 50 million dollar LottoMax main jackpot last Friday night
( 7/49 game ) was shared by 3 winners for a total of $16,666,666.70 each!
There was also an additional 38 million dollars above and beyond the 50
million maximum main jackpot, for which 38 more combos were drawn in an
effort to facilitate a maximum of 38 winners more as the newest
millionaires, at 1 million dollars per extra combo prize money each, if they
didn't have to share it with anyone else bearing the same ticket combo.
This secondary phase of the draw produced 14 more million dollar winners,
and then 8 more winners got to share 4 more of the 1 million dollar prizes
at $500,000.00 each because there were 2 winners to share each extra
million...No one hit any of the remaining 22 X one-million-dollar combos
which were drawn, so they will be available for winnings in the next jackpot
on the next Friday.
What a bummer...2 of the main jackpot winners should never have played
that combo, so as to give it all to just one winner...unless they were all
quick-pick tickets. That's what I'm understanding you to be saying, Nigel.
No, we wouldn't know that this particular combo would have won, but you are
searching for a way to filter out the shared-jackpot possibilities in order
to prevent this from happening, as I understand it...so...WTF? Please
explain if I have your shared-jackpot-filter concept incorrect.
Jack
nigel
> On 4/18/2011 3:12 AM, nigel wrote:
>
>> Jack Ricci wrote:
>>
>>>
>>> "nigel" wrote in message
>>> news:4uWdndJ6SI_rkzbQ...@brightview.co.uk...
>>>
>>> If anyone fancies writing software to filter out combos which are likely
>>> to result in a shared jackpot, note that the above are only first-order
>>> effects, and the filters may need to change from lottery to lottery to
>>> reflect the sophistication of the players.
>>>
>>>
>>> Evil Nigel
>>>
>>> --------------------------------------------------------------------------------------------------------------------------
>>>
>>>
>>>
>>> ...It blows my mind to see that anyone would want to filter out the
>>> winning of a shared jackpot.
>>>
>>> Jack
>>>
>>>
>>
>> It blows my mind that anyone would know the winning numbers in advance
>> so they'd know not to filter them out.
>>
>> Evil Nigel
>>
>
> Many years ago I applied some brute force filtering and would have won
> jackpot if I had bought the 92 tickets but I didn't really believe in
> the filtering method.
Did you continue to monitor how the filtered tickets would have fared?
> There was a lesson to be learned but I never figured it out because
> I was and still am blown away.
>
> All I have left of my shattered dream is a bunch of buttons to click :(
If I had a quid in my pocket to spend on Wednesday's UK Lottery draw,
given the option of a 1 in 14 million chance of winning £240 by buying
the combo 1,2,3,4,5,6 (£2.4 million jackpot shared between 10000 people)
or a 1 in 14 million chance of winning a likely £2.4 million by buying
the combo 1,24,29,30,43,49 (£2.4 million jackpot unshared), I'm quite
happy to see other punters follow Jack's philosophy and buy 1,2,3,4,5,6
because they want to share the jackpot.
Evil Nigel
Gerry
> Gerry wrote:
>
>> On 4/18/2011 3:12 AM, nigel wrote:
>>
>>> Jack Ricci wrote:
>>>
>>>>
>>>> "nigel" wrote in message
>>>> news:4uWdndJ6SI_rkzbQ...@brightview.co.uk...
>>>>
>>>> If anyone fancies writing software to filter out combos which are
>>>> likely
>>>> to result in a shared jackpot, note that the above are only first-order
>>>> effects, and the filters may need to change from lottery to lottery to
>>>> reflect the sophistication of the players.
>>>>
>>>>
>>>> Evil Nigel
>>>>
>>>> --------------------------------------------------------------------------------------------------------------------------
>>>>
>>>>
>>>>
>>>> ...It blows my mind to see that anyone would want to filter out the
>>>> winning of a shared jackpot.
>>>>
>>>> Jack
>>>>
>>>>
>>>
>>> It blows my mind that anyone would know the winning numbers in advance
>>> so they'd know not to filter them out.
>>>
>>> Evil Nigel
>>>
>>
>> Many years ago I applied some brute force filtering and would have won
>> jackpot if I had bought the 92 tickets but I didn't really believe in
>> the filtering method.
>
> Did you continue to monitor how the filtered tickets would have fared?
No but it took a while to move on.
>
>> There was a lesson to be learned but I never figured it out because
>> I was and still am blown away.
>>
>> All I have left of my shattered dream is a bunch of buttons to click :(
>
> If I had a quid in my pocket to spend on Wednesday's UK Lottery draw,
> given the option of a 1 in 14 million chance of winning £240 by buying
> the combo 1,2,3,4,5,6 (£2.4 million jackpot shared between 10000 people)
> or a 1 in 14 million chance of winning a likely £2.4 million by buying
> the combo 1,24,29,30,43,49 (£2.4 million jackpot unshared), I'm quite
> happy to see other punters follow Jack's philosophy and buy 1,2,3,4,5,6
> because they want to share the jackpot.
>
> Evil Nigel
>
I don't want to share the JP with anybody. I'm not even sure if I
would tell my wife.
nigel
Jack Ricci wrote:
<snip>
>
> That's a double negative...You are still hoping to filter out the
> combos that would produce a shared jackpot. I would only do that if
> shared jackpots occurred only once a decade, so as to need fewer combos
> to play each game only if the past history data demonstrated that there
> would be a likelihood of a shared jackpot combo not occurring in a draw
> but once in a decade, if that were possible.
The profile of number of jackpot winners per draw is a function of the
frequency with which that number of people choose the same numbers.
If 3 people share the jackpot 25% of the time, then 25% of the tickets
on average are bought by three people. More or less people buying the
same ticket does not influence the probability that the ticket is drawn,
unless you're a disciple of Harry Scott or a Lottery Puppeteer.
> However, those shared jackpot combos do occur more often than just
> once in a decade, and those shared-jackpot combos which your software (
> or other method of ) picks have just as good a likelihood of being drawn
> as the actual combos which you eventually pay to play, so that makes
> your above statements a redundant claim.
Choosing combos which mean you're less likely to have to share a jackpot
does not influence the probability those combos are drawn, it means
you're likely to win more if they are drawn.
> If you believe in or have faith in your number picking
> scheme(s)/method(s), then the shared jackpot filter sucks.
That is true.
> Our Canadian 50 million dollar LottoMax main jackpot last Friday night
> ( 7/49 game ) was shared by 3 winners for a total of $16,666,666.70
> each! There was also an additional 38 million dollars above and beyond
> the 50 million maximum main jackpot, for which 38 more combos were drawn
> in an effort to facilitate a maximum of 38 winners more as the newest
> millionaires, at 1 million dollars per extra combo prize money each, if
> they didn't have to share it with anyone else bearing the same ticket
> combo.
>
> This secondary phase of the draw produced 14 more million dollar
> winners, and then 8 more winners got to share 4 more of the 1 million
> dollar prizes at $500,000.00 each because there were 2 winners to share
> each extra million...No one hit any of the remaining 22 X
> one-million-dollar combos which were drawn, so they will be available
> for winnings in the next jackpot on the next Friday.
>
> What a bummer...2 of the main jackpot winners should never have played
> that combo, so as to give it all to just one winner...unless they were
> all quick-pick tickets. That's what I'm understanding you to be saying,
> Nigel.
No, the point of trying to choose combos that won't result in a shared
jackpot is that you're taking advantage of less savvy punters. If
everyone used the same filters it would be self-defeating.
Take Saturday's UK numbers - 3,34,40,41,44,49. In the first year or two
of the lottery that would have been a very good combination to choose
because punters were very ignorant about the choices other punters were
likely to make.
The population is now partially more sophisticated, and a significant
number know to avoid picking all birthday numbers. This has led to a
group of contrarians now picking a preponderance of non-birthday numbers
resulting in 3,34,40,41,44,49 becoming a relatively poor choice.
(Okay, they won £4 million each because of the triple rollover, but on a
typical Saturday they would have won £1 million, a sum I consider
inadequate to be life-changing.)
> No, we wouldn't know that this particular combo would have won,
> but you are searching for a way to filter out the shared-jackpot
> possibilities in order to prevent this from happening, as I understand
> it...so...WTF? Please explain if I have your shared-jackpot-filter
> concept incorrect.
I think you have it wrong - the point is to take advantage of
information you know about the likely choices of other punters who don't
care to avail themselves of the same information.
>
> Jack
>
If, just before the draw, you were given a list of combos and a count of
how many punters had chosen each one, then you were allowed to buy one,
or ten (or some other number significantly smaller than the total number
of combos) entries of your own, wouldn't you try to take advantage of
that knowledge?
You don't have that luxury in real life but with a little bit of
analysis and common sense you can arrive at something almost as good.
Evil Nigel
Dionysus
> On 4/18/2011 3:12 AM, nigel wrote:
>
>
>
>
>
> > Jack Ricci wrote:
>
> >> "nigel" wrote in message
> >>news:4uWdndJ6SI_rkzbQ...@brightview.co.uk...
>
> >> If anyone fancies writing software to filter out combos which are likely
> >> to result in a shared jackpot, note that the above are only first-order
> >> effects, and the filters may need to change from lottery to lottery to
> >> reflect the sophistication of the players.
>
> >> Evil Nigel
>
>
> >> ...It blows my mind to see that anyone would want to filter out the
> >> winning of a shared jackpot.
>
> >> Jack
>
> > It blows my mind that anyone would know the winning numbers in advance
> > so they'd know not to filter them out.
>
> > Evil Nigel
>
> Many years ago I applied some brute force filtering and would have won
> jackpot if I had bought the 92 tickets but I didn't really believe in
> the filtering method.
>
> There was a lesson to be learned but I never figured it out because
> I was and still am blown away.
>
>
> - Show quoted text -
May I HAVE THE HONOR to know what kind of filter is that??
Dionysus
> Gerry wrote:
> > On 4/18/2011 3:12 AM, nigel wrote:
>
> >> Jack Ricci wrote:
>
> >>> "nigel" wrote in message
> >>>news:4uWdndJ6SI_rkzbQ...@brightview.co.uk...
>
> >>> If anyone fancies writing software to filter out combos which are likely
> >>> to result in a shared jackpot, note that the above are only first-order
> >>> effects, and the filters may need to change from lottery to lottery to
> >>> reflect the sophistication of the players.
>
> >>> Evil Nigel
>
>
> >>> ...It blows my mind to see that anyone would want to filter out the
> >>> winning of a shared jackpot.
>
> >>> Jack
>
> >> It blows my mind that anyone would know the winning numbers in advance
> >> so they'd know not to filter them out.
>
> >> Evil Nigel
>
> > Many years ago I applied some brute force filtering and would have won
> > jackpot if I had bought the 92 tickets but I didn't really believe in
> > the filtering method.
>
> Did you continue to monitor how the filtered tickets would have fared?
>
> > There was a lesson to be learned but I never figured it out because
> > I was and still am blown away.
>
> > All I have left of my shattered dream is a bunch of buttons to click :(
>
> If I had a quid in my pocket to spend on Wednesday's UK Lottery draw,
> given the option of a 1 in 14 million chance of winning 240 by buying
> the combo 1,2,3,4,5,6 ( 2.4 million jackpot shared between 10000 people)
> or a 1 in 14 million chance of winning a likely 2.4 million by buying
> the combo 1,24,29,30,43,49 ( 2.4 million jackpot unshared), I'm quite
> happy to see other punters follow Jack's philosophy and buy 1,2,3,4,5,6
> because they want to share the jackpot.
>
>
> - Show quoted text -
I just wish I knew 1 4 9 0 3 ? before as 6 last digits.
AT LEAST there is some chance to try match5.
Colin Fairbrother
game is 0.0000007
The probability of getting 8 random lines for a 6/49 Lotto game with
the optimum coverage of 14.82994 is 0.000000000000000006
The difference is massive as far as getting the best coverage for 8
lines by random selections over a calculated set with unique integers.
Even though It makes no difference as to winning first prize there is
the satisfaction of having given it your best shot for the sub-
prizes.
Colin Fairbrother
http://LottoPoster.com
Dionysus
there lays more chance to get match4 and match5
Colin Fairbrother
the set of 8 lines with unique integers and a 3if6 coverage of
14.82994% we have the following: -
Prize 4 Prize 3 Draws
0 0 85
0 1x 14
1x 0 1
For a typical random selection of 8 lines with 3if6 coverage of
13.97834% we have the following: -
Prize 4 Prize 3 Draws
0 0 86
0 1x 12
0 2x 1
1 0 1
We see the partial cover gives more draws with a win (15) with 14
single three wins and the random selections gives more draws with
multiple wins (1). Yield is the same for both. Playing a set with a
greater number of lines can give a marginally better separation.
What does it all mean? It means most of the rubbish put forward as to
improving the chances of winning do precisely the opposite by not
using all the integers for the game and repeating the paying subsets.
A notable exception as I have pointed out before is the
C(12,6,4,6,9)-22.
Colin Fairbrother
http://LottoPoster.com
Colin Fairbrother
coverage of sets from a Lotto history where the draws are unique and
consecutive. You would need to import the data into a record set,
dataset or array and loop your way though for the range selected in
say a drop-down sending the range data in an array to your coverage
function. The coverage for 8 lines with 48 of the possible 49 integers
is 14.82994% which is the maximum possible.
For a range of 8 draws over a history of 1588 draws in the UK Lotto we
get for the 198 sets: -
Average Coverage: 13.98414%
Maximum Coverage: 14.42399%
Minimum Coverage: 13.17304%
Standard Deviation: 0.2454
Variance: 0.06024
Any 6/49 Lotto game that departed significantly from these figures
over the same number of draws would be cause for concern. Importantly,
random selections are consistent in coverage and from my earliest
posts on the internet in 2004 I have maintained the benchmark for
testing any structured set of Lotto numbers is Random Selections.
As mentioned before there is no significant difference in Yield
between the average coverage set from Random Selections (Lotto
History) and that of the maximum possible coverage.
Colin Fairbrother
http://LottoPoster.com
nb Variance is the average of the squared differences from the mean or
average. Standard Deviation is the square root of the variance. Hence
square root of 0.06024 gives a Standard Deviation of 0.2454.
Colin Fairbrother
which told me programatically was spelt wrong - I clicked change
without closely looking.